Geography Reference
In-Depth Information
Taylor expansion:
l =
= L + l t x t x + l t y t y + l t z t z + l α α + l β β + l γ γ + l s s + l A δA + l E δE 2 ,
(21.20)
b =
= B + b t x t x + b t y t y + b t z t z + b α α + b β β + b γ γ + b s s + b A δA + b E δE 2 ,
subject to
∂l
∂t x ( t x = t y = t z =0 = β = γ =0 ,s =0 ,A 1 = a 1 ,E 2 = e 2 )
l t x :=
(21.21)
etc. and
a 1 ,δE 2 := E 2
e 2 , δE =(2 E ) 1 δE 2 .
δA := A 1
(21.22)
Box 21.4 (Curvilinear conformal coordinate transformation (datum transformation) extended
by ellipsoid parameters close to identity, Jacobi matrix).
t x
t y
t z
α
β
γ
s
δA
δE 2
y = l
=A
L
+O 2 lb =A x +O 2 x .
(21.23)
b
B
Jacobi matrix:
A:=
( l,b )
( t x ,t y ,t z ,α,β,γ,s,A 1 ,E 2 )
2 × 9 ,
taylor R
(21.24)
t x = t y = t z = α = β = γ = s =0 1 = a 1 ,E 2 = e 2
taylor :=
{
}
.
Chain Jacobi matrix:
A:=J 23 J 1 = ( l,b )
( x, y, z )
( x, y, z )
( t x ,t y ,t z ,α,β,γs,A 1 ,E 2 )
,
(21.25)
taylor
taylor
( x, y, z )
( l,b,h )
1
= ( l,b,h )
( x, y, z )
,
 
Search WWH ::




Custom Search